Hyperarithmetical Categoricity of the Boolean Algebra $\mathfrak{B}(\omega^{\alpha}\times\eta)$
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 12 (2012) no. 3, pp. 35-45
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We consider $\Delta^{0}_{\beta}$-categoricity in Boolean algebras. We prove the following theorem: if $\delta$ is a limit ordinal or 0, $n\in\omega$, and $\delta+n\geqslant 1$, then the Boolean algebra $\mathfrak{B}(\omega^{\delta+n}\times\eta)$ is $\Delta^{0}_{\delta+2n+1}$-categorical and not $\Delta^{0}_{\delta+2n}$-categorical.
Keywords:
Boolean algebra, categoricity, back-and-forth relations.
@article{VNGU_2012_12_3_a3,
author = {N. A. Bazhenov},
title = {Hyperarithmetical {Categoricity} of the {Boolean} {Algebra} $\mathfrak{B}(\omega^{\alpha}\times\eta)$},
journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
pages = {35--45},
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volume = {12},
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N. A. Bazhenov. Hyperarithmetical Categoricity of the Boolean Algebra $\mathfrak{B}(\omega^{\alpha}\times\eta)$. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 12 (2012) no. 3, pp. 35-45. http://geodesic.mathdoc.fr/item/VNGU_2012_12_3_a3/